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straight line D is tangent at A

Source: IMO 1980 Luxembourg, problem 4

May 6, 2004
geometrycircumcirclecirclesbisectorIMO Shortlist

Problem Statement

Two circles C1C_{1} and C2C_{2} are (externally or internally) tangent at a point PP. The straight line DD is tangent at AA to one of the circles and cuts the other circle at the points BB and CC. Prove that the straight line PAPA is an interior or exterior bisector of the angle ∠BPC\angle BPC.
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